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A novel modiied method for obtaining approximate solutions to diicult optimization problems within the neural network paradigm is presented. We consider the graph partition and the travelling salesman problems. The key new ingredient is a reduction of solution space by one dimension by using graded neurons, thereby avoiding the destructive redundancy that(More)
  • Bo Söderberg
  • 2002
We present and investigate an extension of the classical random graph to a general class of inhomogeneous random graph models, where vertices come in different types, and the probability of realizing an edge depends on the types of its terminal vertices. This approach provides a general framework for the analysis of a large class of models. The generic(More)
A strategy for nding approximate solutions to discrete optimization problems with inequality constraints using mean eld neural networks is presented. The constraints x 0 are encoded by x(x) terms in the energy function. A careful treatment of the mean eld approximation for the self-coupling parts of the energy is crucial, and results in an essentially(More)
  • Bo Söderberg
  • 2003
We propose and investigate a unifying class of sparse random graph models, based on a hidden coloring of edge-vertex incidences, extending an existing approach, random graphs with a given degree distribution, in a way that admits a nontrivial correlation structure in the resulting graphs. The approach unifies a number of existing random graph ensembles(More)
We demonstrate how to generalize two of the most well-known random graph models, the classic random graph, and random graphs with a given degree distribution, by the introduction of hidden variables in the form of extra degrees of freedom, color, applied to vertices or stubs (half-edges). The color is assumed unobservable, but is allowed to affect edge(More)
  • Bo Söderberg
  • 2003
We investigate in some detail a recently suggested general class of ensembles of sparse undirected random graphs based on a hidden stub coloring, with or without the restriction to nondegenerate graphs. The calculability of local and global structural properties of graphs from the resulting ensembles is demonstrated. Cluster size statistics are derived with(More)
Large-scale pattern formation is a frequently occurring phenomenon in biological organisms, and several local interaction rules for generating such patterns have been suggested. A mechanism driven by feedback between the plant hormone auxin and its polarly localized transport mediator PINFORMED1 has been proposed as a model for phyllotactic patterns in(More)
In a recent paper (Gisl en, Peterson and SS oderberg 1989) a convenient encoding and an eecient mean eld algorithm for solving scheduling problems using a Potts neural network was developed and numerically explored on simpliied and synthetic problems. In this work the approach is extended to realistic applications both with respect to problem complexity and(More)
A convenient mapping and an eecient algorithm for solving scheduling problems within the neural network paradigm is presented. It is based on a reduced encoding scheme and a mean eld annealing prescription, which was recently successfully applied to TSP. Most scheduling problems are characterized by a set of hard and soft constraints. The prime target of(More)